NDLI: Shrinkage estimation of high dimensional covariance matrices

Content Provider	IEEE Xplore Digital Library
Author	Yilun Chen Wiesel, A. Hero, A.O.
Copyright Year	2009
Description	Author affiliation: Department of EECS, University of Michigan, Ann Arbor, 48109, USA (Yilun Chen; Wiesel, A.; Hero, A.O.)
Abstract	We address covariance estimation under mean-squared loss in the Gaussian setting. Specifically, we consider shrinkage methods which are suitable for high dimensional problems with small number of samples (large p small n). First, we improve on the Ledoit-Wolf (LW) method by conditioning on a sufficient statistic via the Rao-Blackwell theorem, obtaining a new estimator RBLW whose mean-squared error dominates the LW under Gaussian model. Second, to further reduce the estimation error, we propose an iterative approach which approximates the clairvoyant shrinkage estimator. Convergence of this iterative method is proven and a closed form expression for the limit is determined, which is called the OAS estimator. Both of the proposed estimators have simple expressions and are easy to compute. Although the two methods are developed from different approaches, their structure is identical up to specific constants. The RBLW estimator provably dominates the LW method; and numerical simulations demonstrate that the OAS estimator performs even better, especially when n is much less than p.
Starting Page	2937
Ending Page	2940
File Size	246651
Page Count	4
File Format	PDF
ISBN	9781424423538
ISSN	15206149
DOI	10.1109/ICASSP.2009.4960239
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-04-19
Publisher Place	Taiwan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Covariance matrix Iterative methods Numerical simulation Array signal processing Ambient intelligence Error analysis Estimation error Convergence Genomics Bioinformatics mean-squared loss Shrinkage covariance estimation Rao-Blackwell
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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